Helping Children Learn Mathematics Through Multiple Intelligences and Standards for School Mathematics.Many approaches can be used when teaching mathematics to young children, and many theories and philosophies of learning address empowering children to learn mathematics. Whatever method is chosen, however, children's varied learning styles, strengths, experiences, and perspectives must be considered. To achieve that goal, it is important to recognize that not all children learn in the same way, and that children have multiple means of learning. Multiple Intelligences Howard Howard, English noble family. Landowners in Norfolk from the 13th cent., the Howards obtained the duchy of Norfolk through the marriage of Sir Robert Howard to Margaret Mowbray, daughter of Thomas Mowbray, 1st duke of Norfolk. Gardner's multiple intelligence theory (1983) states that children employ a variety of intelligences in learning situations. He originally proposed that children learn through seven intelligences (see Table 1). Table 1 SUMMARY OF GARDNER'S ORIGINAL MULTIPLE INTELLIGENCES
INTELLIGENCE DESCRIPTION
Linguistics Words/Language: the ability to use words
correctly and comfortably, either orally or in
writing, to express meaning
Logical- Logic/Mathematics: the ability to use numbers
Mathematical correctly and effectively; to think
inductively or deductively; to categorize,
classify, and generalize
Spatial Visual: the ability to understand, interpret,
and model the visual world; to represent
spatial information effectively
Bodily- Body/Physical: the ability to use physical
Kinesthetic means to represent ideas and feelings
Musical Music: the ability to understand and use
musical concepts in a perceptive or
technical sense; to develop
an appreciation for music
Interpersonal People/Relationships: the ability to
relate to and understand people; to possess
good social and leadership skills
Intrapersonal Self: the ability to use self-understanding
and self-knowledge; to monitor the self; to
be self-disciplined
(Armstrong, 1994)
Children might have strength in one or more intelligences, which serve as mechanisms for learning and lead to cognitive cog·ni·tive adj. 1. Of, characterized by, involving, or relating to cognition. 2. Having a basis in or reducible to empirical factual knowledge. ability. Each child may use a variety of these intelligences to learn mathematics concepts and skills, not just the logical-mathematical. The activity and lesson ideas presented in this article represent experiences from which all children can benefit, regardless of the intelligences they most favor. Therefore, it is not necessary to attempt to categorize cat·e·go·rize tr.v. cat·e·go·rized, cat·e·go·riz·ing, cat·e·go·riz·es To put into a category or categories; classify. cat children by intelligence, but only to provide for them a multitude MULTITUDE. The meaning of this word is not very certain. By some it is said that to make a multitude there must be ten persons at least, while others contend that the law has not fixed any number. Co. Litt. 257. of learning opportunities. Standards for School Mathematics In April 2000, the National Council of Teachers of Mathematics The National Council of Teachers of Mathematics (NCTM) was founded in 1920. It has grown to be the world's largest organization concerned with mathematics education, having close to 100,000 members across the USA and Canada, and internationally. (NCTM NCTM National Council of Teachers of Mathematics NCTM Nationally Certified Teacher of Music NCTM North Carolina Transportation Museum NCTM National Capital Trolley Museum NCTM Nationally Certified in Therapeutic Massage ) unveiled its new Principles and Standards for School Mathematics Principles and Standards for School Mathematics was a document produced by the National Council of Teachers of Mathematics [1] in 2000 to set forth a national vision for precollege mathematics education in the US and Canada. (NCTM, 2000). Of the 10 standards, five are content-oriented and five are process-oriented. This article focuses on the process standards: 1) Problem Solving problem solving Process involved in finding a solution to a problem. Many animals routinely solve problems of locomotion, food finding, and shelter through trial and error. , 2) Reasoning and Proof, 3) Communication, 4) Connections, and 5) Representation. They serve as a framework for utilizing the multiple intelligences that children bring to mathematics learning. Each process standard is briefly described in Table 2. Table 2 SUMMARY OF THE NATIONAL COUNCIL OF TEACHERS OF MATHEMATICS PROCESS STANDARDS (NCTM, 2000)
STANDARD DESCRIPTION
Instructional programs should enable
all students to ...
Problem * build new mathematical knowledge.
Solving * solve problems in mathematics and in
other contexts.
* apply and modify a variety of
problem-solving strategies.
* monitor and reflect on the
problem-solving process.
Reasoning * recognize reasoning and proof as
& Proof foundations of mathematics.
* make and investigate conjectures and
hypotheses.
* develop and assess arguments and proofs.
* choose and use a variety of proof
techniques.
Communication * organize and consolidate mathematical
thinking.
* communicate mathematical thinking
coherently and clearly.
* analyze and assess the mathematical
thinking of others.
* use mathematical language to express
ideas.
Connections * recognize and apply connections among
mathematical ideas.
* understand how the idea "parts" create
the "whole."
* recognize and apply mathematics in
other contexts and areas.
Representation * create and use mathematical
representations.
* choose, apply, and translate among
representations.
* use representations to model and
understand mathematical ideas.
(NCTM, 2000)
The ideas presented here for mathematics lessons and activities are designed to capitalize on Cap´i`tal`ize on` v. t. 1. To turn (an opportunity) to one's advantage; to take advantage of (a situation); to profit from; as, to capitalize on an opponent's mistakes s>. children's use of the seven intelligences for learning. Ideally, they will initiate INITIATE. A right which is incomplete. By the birth of a child, the husband becomes tenant by the curtesy initiate, but his estate is not consummate until the death of the wife. 2 Bouv. Inst. n. 1725. development of more comprehensive classroom experiences. Most of the ideas build on common experiences during the process of teaching mathematics. The author hopes to create a structure, based on the NCTM process standards, for providing opportunities for all children to learn mathematics through those intelligences that serve the children best. Multiple Intelligences and Problem Solving To consider problem solving as "the central focus of the mathematics curriculum" (NCTM, 1989) evokes a multitude of heuristics heu·ris·tic adj. 1. Of or relating to a usually speculative formulation serving as a guide in the investigation or solution of a problem: , plans, methods, and strategies. The multiple intelligences theory provides a platform from which to build on learners' diverse problem-solving problem-solving n → resolución f de problemas; problem-solving skills → técnicas de resolución de problemas problem-solving n → characteristics and strengths. An understanding of the multiple intelligences approach is critical, because problem solving involves a person participating in a task or experience for which the answer or solution is not readily known or available (Krulik & Rudnick, 1993). Hence, each child has the potential of using a unique approach when solving a problem. Consider the ideas in Table 3 for approaching mathematics through problem solving. Table 3 MULTIPLE INTELLIGENCES AND PROBLEM SOLVING
INTELLIGENCE PROBLEM SOLVING
Children can ...
Linguistic * write stories as contexts for word
problems; trade stories (and problems)
with classmates; read stories; solve
problems, discuss solutions.
* record journal entries related to the
problem-solving experience, and, with
instruction, be able to explain their
way of thinking about problems.
* explain problem-solving strategies
(e.g., working backward, trying a simpler
problem) to each other.
Logical- * sort polygons into separate groups
Mathematical according to a rule known only by a
leader; the leader only answers "yes"
or "no" to the children's question as
they search for the leader's rule for
classifying the polygons.
* gather, record, and use numerical data
to solve problems.
* solve problems with numbers used in
various contexts (e.g., ordinal numbers,
nominal numbers).
Spatial * hypothesize about the identity of
geometrical solids according to "clues"
given by a leader (e.g., "It is a solid
with 12 edges. What is it?").
* use drawings and diagrams as
problem-solving strategies.
* build physical models as tools for
solving problems (e.g., use toothpicks
for network problems).
* create a problem-solving board game
with manipulative pieces.
Bodily- * engage in simulations to demonstrate
Kinesthetic and model problem contexts.
* use dramatization as a strategy for
solving problems.
* use bodily movement to express feelings
and attitudes about problem solving.
Musical * find and extend patterns in music
(e.g., Given the scales for several
measures in sequence, students should
be able to determine the next measure)
(NCTM, 1997).
* look for patterns as a problem-solving
strategy.
* translate problem-solving strategies
to a musical tune to help recall
strategies.
Interpersonal * write or find problems that they think
can be solved by their classmates (these
problems can be used for explorations).
* solve problems through cooperative
learning.
* be leaders or guides of a
problem-solving team.
Intrapersonal * consider a set of problems to be solved
and conjecture about their own abilities
or confidence to solve the problems.
* set goals for growth in problem solving.
* reflect on and discuss reasons for
performing certain actions during the
problem-solving process, orally or in
writing.
Multiple Intelligences and Reasoning and Proof Reasoning means using available information and prior knowledge to make sense of an idea or phenomenon. Estimating, questioning, hypothesizing, and conjecturing are some of the components of reasoning (NCTM, 1989). One of the best ways to improve children's reasoning skills is to create opportunities and situations that encourage them to use reason. In addition, children should be encouraged to justify, or "prove," their reasons and explanations relevant to a mathematical situation. They should be challenged to support or refute re·fute tr.v. re·fut·ed, re·fut·ing, re·futes 1. To prove to be false or erroneous; overthrow by argument or proof: refute testimony. 2. conclusions with well thought-out thought-out adj → durchdacht evidence and suggestions. The suggestions in Table 4 provide reasoning and proof opportunities for children with various learning styles. Many other reasoning and proof experiences can be added to this list. Table 4 MULTIPLE INTELLIGENCES AND REASONING AND PROOF
INTELLIGENCE REASONING AND PROOF
Children can ...
Linguistic * discuss patterns in real-world and
mathematical situations.
* provide written and oral
justifications of their learning
actions.
* express their arguments in ways
that make sense to others.
* summarize and explain the
justifications of others.
Logical- * develop mathematical conjectures and
Mathematical hypotheses.
* generalize mathematical conclusions
(e.g., The sum of zero and any number
is that number).
* be challenged to answer questions
such as "Why is this true?" and "How
can you prove that your answer is
valid?"
* explore the mathematical properties
of calendars, and make conjectures
about certain phenomena.
Spatial * use paper folding or cutting to
prove concepts (e.g., 1/2 = 2/4).
* build models to prove relationships
between concepts (e.g., What is the
relationship between the concept of
square and the concept of rectangle?).
* analyze objects for useful
information.
Bodily- * use their bodies to reason about
Kinesthetic concepts (e.g., proportion,
measurement).
* act out (dramatize) in order to
demonstrate their understanding and
reasoning.
* consider why a base 10 numeration
system is common in the United
States, while other cultures use a
base 20 system.
Musical * make conjectures as to whether
or not patterns are infinite (e.g.,
compare patterns to songs that have
patterned rounds that "never end").
* write a song (to a known tune, if
necessary) that expresses
understanding for a mathematical
concept.
Interpersonal * listen to conjectures and hypotheses
presented by others and communicate
accordingly.
* collaborate with others to develop
arguments and proofs.
* compare justifications to look for
common ideas.
* engage in debates and discussions
with classmates.
Intrapersonal * evaluate the validity of
conjecture(s) after an experiment.
* be challenged to avoid making
groundless hypotheses and conjectures.
* use personal knowledge and
previous experiences to build a
basis for a conjecture.
Multiple Intelligences and Communication Communication is a key component of an effective classroom. Oral discourse For other uses, see Discourses. Discourse is communication that goes back and forth (from the Latin, discursus, "running to and fro"), such as debate or argument. The term is used in semantics and discourse analysis. , written work, and dramatization dram·a·ti·za·tion n. 1. The act or art of dramatizing: the dramatization of a novel. 2. A work adapted for dramatic presentation: provide opportunities for children to share with, and learn from, others. Communication also offers an opportunity for children to be part of an active community of learners, wherein where·in adv. In what way; how: Wherein have we sinned? conj. 1. In which location; where: the country wherein those people live. 2. each person's input is valued and respected. Table 5 includes ideas for enhancing communication in the classroom. Table 5 MULTIPLE INTELLIGENCES AND COMMUNICATION
INTELLIGENCE COMMUNICATION
Children can ...
Linguistic * respond to prompts for writing with, and
about, mathematics and mathematics
learning experiences.
* read and develop stories about the
mathematics they are studying.
* engage in discourse about mathematics
and indicate that they can correctly use
mathematical terms.
* explain mathematical terms to children
whose first language is not English;
English as Second Language students
will be able to share their mathematical
terms and labels with
classmates.
Logical- * express their understanding of the
Mathematical magnitude of numbers and their
interpretations of the uses of numbers
through written and oral assignments
(Explore the distance between the sun and
the earth using everyday objects as
arbitrary measurements: e.g., How many
cars, if positioned bumper-to-bumper,
would it take to reach from the sun to
the earth?).
* exercise critical thinking through
open-ended discussions.
* develop and use categories to classify
written and oral mathematical information.
Spatial * describe characteristics of
two-dimensional shapes and
three-dimensional objects as part of a
geometry assessment.
* use concept mapping to communicate
their patterns of thinking.
* write and verbalize descriptions of
mathematical objects.
* draw and use objects to convey ideas
about mathematical concepts.
Bodily- * use "body language" or charades to
Kinesthetic convey a mathematical message to
classmates.
* use the body to answer questions or
engage in an exploration (e.g., raise
hand, join a specific group, move to a
certain place in the room, place self in
the correct position in some ordinal
group--arranged by height, age, etc.).
Musical * listen to popular children's songs to
detect the mathematical concepts therein
(e.g., "This Old Man"--counting song;
"If You're Happy and You Know
It"--pattern song).
* write songs to communicate mathematical
ideas to others.
* listen to counting songs from other
cultures and languages.
Interpersonal * listen to others share their
mathematical ideas.
* share journal entries or other writings,
and assist each other with developing
questions for the teacher to eliminate
misunderstandings.
* share communicative roles in
cooperative groups (e.g., recorder,
reporter etc.)
* consider the validity of different
mathematical points of view, as well as
others' perspectives.
Intrapersonal * review problem-solving experiences and
provide reflections about their thinking
during the process of solving the
problems.
* keep a personal journal of mathematical
experiences.
* explain and justify their answers.
* discuss with others the thinking behind
a mathematical learning experience.
* describe feelings and attitudes about
mathematics.
Multiple Intelligences and Connection Making mathematical connections within mathematics, and between mathematics and other disciplines (NCTM, 1989, 2000), is important to helping children view mathematics as an applicable tool. Because children learn differently and benefit from operating within the strength of one or more intelligences, mathematical connections can help children view mathematics from different perspectives. Table 6 offers some insight into how connections can be addressed for the multiple intelligences that children bring into the classroom. Children also need to gain a perspective of mathematics as a body of knowledge that is related to other subjects in multiple ways. Curriculum integration is one tool for making these connections explicit. Table 6 MULTIPLE INTELLIGENCES AND CONNECTIONS
INTELLIGENCE CONNECTIONS
Children can ...
Linguistic * explore and discuss relationships
between mathematics and other subjects
(e.g., mathematics and art).
* write about relationships between
mathematical concepts (e.g., addition
and subtraction).
Logical- * explore relationships and differences
Mathematical between numbers (e.g., prime and
composite, odd and even, etc.).
* study the uses and interpretations of
various numbers (e.g., How are negative
numbers used in various jobs? How are
numbers used in sports?).
* categorize and classify numbers
(e.g., real, rational, integer, etc.).
Spatial * explore relationships between and
among two-dimensional shapes.
* explore relationships between and
among three-dimensional objects.
* explore the uses of mathematics in
architecture (e.g., Why would people
build round houses versus
rectangular houses?)
Bodily- * explore relationships of the body
Kinesthetic (e.g., One's arm span is an indication
of one's height).
* investigate connections between the
body and various restrictions (e.g.,
the maximum number of
people that can ride an elevator at
one time).
* use body characteristics for learning
about disjointed or intersecting groups.
Musical * explore the connection between music
and mathematics (e.g., both use terms
like "half," "quarter," "whole").
* use musical notes to learn fractions
(e.g., How many half notes equal a
whole note? How many quarter notes
equal a half note?).
* create a mathematics musical in
connection with the music program.
Interpersonal * engage in group explorations related
to studying mathematics, as it is
applied in other subjects and contexts.
* explain to others, coherently and
clearly, the connections between
mathematical concepts (e.g., the
connection between circumference and
diameter of a circle).
* lead a peer group discussion about
various mathematical connections within
and outside the realm
of mathematics.
Intrapersonal * be challenged to use prior knowledge
to solve problems.
* explore opportunities for connections
between mathematics and other subjects
in their own environment (e.g., homes,
neighborhoods).
* consider ways in which they use
mathematics outside of the classroom.
Mathematical knowledge and information can be represented in a variety of ways. How children perceive per·ceive v. 1. To become aware of directly through any of the senses, especially sight or hearing. 2. To achieve understanding of; apprehend. , interpret To run a program one line at a time. Each line of source language is translated into machine language and then executed. , and create these representations is an important issue. For example, children benefit from being able to use various representations for solving problems, engaging in projects and discussions, and exploring the world of numbers. Some mathematical information is easier to understand and work with in one representation than in another. Consider the multiplication multiplication, fundamental operation in arithmetic and algebra. Multiplication by a whole number can be interpreted as successive addition. For example, a number N multiplied by 3 is N + N + N. of mixed numbers, for example. It is easier to multiply mul·ti·ply v. 1. To increase the amount, number, or degree of. 2. To breed or propagate. mixed numbers when they are represented as improper fractions improper fraction n. A fraction in which the numerator is larger than or equal to the denominator. improper fraction Noun than it is to leave them as mixed numbers. As children learn mathematics, they should be encouraged to use and create representations that not only make sense to them, but also are efficient means of completing a mathematics task. Table 7 offers some insight into activities that might help children learn about mathematical representations. When considering the ideas presented in the table, think of the many representations of a mathematical concept that are available and how these representations might be useful to children. Table 7 MULTIPLE INTELLIGENCES AND REPRESENTATIONS
INTELLIGENCE REPRESENTATIONS
Children can ...
Linguistic * write numbers in various forms (e.g.,
scientific notation, fractions).
* translate word problems to algebraic
expressions, and vice versa.
* explain their representations of
mathematical ideas.
Logical- * work with numbers in various forms
Mathematical (e.g., fractions, decimals, percents).
* compare representations of numbers
to consider what is most effective or
efficient for communicating an idea.
* use technology (e.g., a computer
spreadsheet) to represent and sort data.
Spatial * develop graphs of algebraic
expressions.
* use diagrams, charts, pictures, and
tables to solve problems.
* use manipulatives and other objects
to represent mathematical concepts
(e.g., base 10 blocks).
Bodily- * model concepts with people (e.g.,
Kinesthetic two groups of four people each has the
same quantity as four groups of two
people each).
* model division by distributing
objects to people.
Musical * collect information on the different
rhythmic patterns of music, and record
the information.
* use concrete objects to model music
rhythms.
* represent rhythms through dance
patterns and drawings.
Interpersonal * engage in discussions about different
mathematical representations.
* participate in group work that
involves the use of various
mathematical representations.
* debate the applicability of various
representations.
Intrapersonal * represent mathematical ideas in
meaningful ways.
* make decisions about which
mathematical representation works best
for given situations.
* organize thinking according to
various representations.
Conclusion The author hopes that this article will initiate dialogue among teachers regarding the multiple intelligences children use for learning mathematics (and other subjects), and the relationship between those intelligences and the new NCTM standards for school mathematics. By paying attention Noun 1. paying attention - paying particular notice (as to children or helpless people); "his attentiveness to her wishes"; "he spends without heed to the consequences" attentiveness, heed, regard to children's varying abilities, interests, and intelligences, we will enhance the quality of mathematics curriculum and instruction. Teachers may want to consider the different ways in which a mathematics concept, skill, or procedure might be approached in light of the different multiple intelligences, while also acknowledging that many of these approaches and multiple intelligences overlap o·ver·lap n. 1. A part or portion of a structure that extends or projects over another. 2. The suturing of one layer of tissue above or under another layer to provide additional strength, often used in dental surgery. v. . Considering how the NCTM 2000 standards overlap with Gardner's multiple intelligences is helpful when developing accessible mathematics curriculum, instruction, and assessment. Table 8 provides an example of how the standards and multiple intelligences can be used together to create meaningful and challenging mathematics experiences for all types of students. Several of the activities presented in Tables 3-7 show the strength of the relationship between the standards and the intelligences. A thorough exploration of the related possibilities can lead to successful and rewarding mathematics teaching and learning experiences in the classroom. Table 8 OVERLAPPING OF GARDNER'S MULTIPLE INTELLIGENCES AND NCTM PROCESS STANDARDS
Linguistic Problem-Solving Reasoning & Proof
* Write stories as * Express arguments
context for word in ways that make
problems. sense to others.
* Write about * Refute / support
problem-solving. a mathematics
idea.
Logical- * Gather, record, * Generalize
Mathematical and use mathematical
numerical conclusions.
to solve
problems.
* Calculate to * Provide non-
solve problems. examples.
Spatial * Use drawings and * Use paper folding
diagrams as and cutting to
problem-solving prove concepts.
strategies.
* Explain a drawn
solution.
Bodily- * Use dramatization * Use parts of the
Kinesthetic as a strategy for body to reason
problem-solving. about concepts
(e.g.,
proportion).
Musical * Translate * Compare patterns
problem-solving to songs that
strategies to a have patterned
musical tune to rounds that
help recall "never end."
strategies.
Interpersonal * Solve problems * Collaborate with
through others to develop
cooperative arguments and
learning. proofs.
* Lead a problem-
solving
excursion.
Intrapersonal * Set goals for * Use personal and
growth in previous
problem-solving. knowledge to
build a basis
for a conjecture.
* Monitor problem-
solving process.
Linguistic Communication Connection
* Respond to * Write about
prompts for relationships
writing with/ between
about mathematical
mathematics. concepts.
* Define terms.
Logical- * Develop and use * Categorize and
Mathematical categories to classify numbers.
classify written
and oral * Explore the use
mathematical of numbers in
information. other
disciplines.
Spatial * Describe * Explore the
characteristics uses of
of two-dimensio- mathematics in
nal shapes and architecture.
three-dimensional
objects. * Describe
classroom
and school.
Bodily- * Use body language * Investigate
Kinesthetic or charades to connections
convey a between body and
mathematical various
message. restrictions in
the world.
Musical * Listen to * Create a
counting songs in mathematics
other cultures musical in
and languages. connection with
the music
program.
Interpersonal * Share communica- * Lead peers in
tive roles in discussions about
cooperative mathematical
groups. connections.
Intrapersonal * Describe feelings * Consider ways in
& attitudes about which mathematics
mathematics. is used in own
life.
* Think aloud.
Linguistic Representation
* Translate word
problems to
algebraic
expressions and
vice versa.
Logical- * Use technology to
Mathematical represent and
sort data.
* Represent numbers
in various ways.
Spatial * Use diagrams,
charts, pictures,
and tables to
solve problems.
Bodily- * Model division by
Kinesthetic distribution of
objects to people.
Musical * Use objects to
model music
rhythms.
* Explore the sound
of concrete
objects.
Interpersonal * Debate the
applicability of
various
representations.
Intrapersonal * Organize thinking
according to
various
representations.
* Use different
representations.
References Armstrong, T. (1994). Multiple intelligences in the classroom. Alexandria Alexandria, city, Egypt Alexandria, Arabic Al Iskandariyah, city (1996 pop. 3,328,196), N Egypt, on the Mediterranean Sea. It is at the western extremity of the Nile River delta, situated on a narrow isthmus between the sea and Lake Mareotis (Maryut). , VA: Association for Supervision and Curriculum Development The Association for Supervision and Curriculum Development, or ASCD, is a membership-based nonprofit organization founded in 1943. It has more than 175,000 members in 135 countries, including superintendents, supervisors, principals, teachers, professors of education, and . Gardner Gardner, city (1990 pop. 20,125), Worcester co., N central Mass.; settled 1764, inc. as a city 1921. Its furniture and lumber industries date from c.1805. Diversified metal and electronics manufactures add to the city's economic base. A state prison is there. , H. (1983). Frames of mind: The theory of multiple intelligences Multiple intelligences is educational theory put forth by psychologist Howard Gardner, which suggests that an array of different kinds of "intelligence" exists in human beings. . New York New York, state, United States New York, Middle Atlantic state of the United States. It is bordered by Vermont, Massachusetts, Connecticut, and the Atlantic Ocean (E), New Jersey and Pennsylvania (S), Lakes Erie and Ontario and the Canadian province of : Basic Books. Krulik, S., & Rudnick, J. A. (1993). Reasoning and problem solving: A handbook
This article is about reference works. For the subnotebook computer, see .
Boston, town (1991 pop. 26,495), E central England, on the Witham River. Boston's fame as a port dates from the 13th cent., when it was a Hanseatic port trading wool and wine. Having recovered from a decline in the 18th and 19th cent. : Allyn & Bacon bacon, flesh of hogs—especially from the sides, belly, or back—that has been preserved by being salted or pickled and then dried with or without wood smoke. . National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics. Reston Reston, uninc. city (1990 pop. 48,556), Fairfax co., N Va., a planned community established in 1961. A suburb of Washington, D.C., Reston is organized in a series of residential villages and commercial areas. , VA: Author. National Council of Teachers of Mathematics. (1997). Student math notes. Reston, VA: Author. National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author. Thomasenia Lott Adams Adams, town (1990 pop. 9,445), Berkshire co., NW Mass., in the Berkshires, on the Hoosic River; inc. 1778. Its manufactures include chemicals, textiles, and paper products. The Berkshire region attracts tourists year-round. is Associate Professor, School of Teaching and Learning, University of Florida University of Florida is the third-largest university in the United States, with 50,912 students (as of Fall 2006) and has the eighth-largest budget (nearly $1.9 billion per year). UF is home to 16 colleges and more than 150 research centers and institutes. , Gainesville Gainesville. 1 City (1990 pop. 84,770), seat of Alachua co., N central Fla.; inc. 1869. The Univ. of Florida is a major source of employment in the city. Agriculture and the manufacture of electronic equipment add to the economy. . |
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